Introduction: Water is the universal solvent inside all cells
and extracellular fluids. Water molecules (H2O) can dissociate
into hydroxide ions (OH-) and hydrogen ions (H+).
Other molecules or parts of molecules have the ability to either give up
hydrogen ions, acids, or accept hydrogen ions, bases. Consequently, we
can characterize any aqueous solution by the concentration of positively
charged hydrogen ions and negatively charged hydroxide ions.

Importance: Many chemical reactions in living cells involve exchanges
of hydrogen ions. Because changes in acidity can affect both the structure
and chemical reactivity of cellular molecules, cells must constantly maintain
an acid-base balance.

Questions: How do we quantify acidity? What affects the buffering
capacity of acids and bases?

Variables:

Keq

equilibrium constant

[X], [Y]

concentrations of reactants

[A], [B]

concentrations of products

d

fraction of a weak acid that is undissociated

Hydrogen ion concentration and pH

Methods:

The dissociation of water into hydroxide and hydrogen ions can be represented
by the following reversible chemical equation:

H2O --->
H+ + OH-

The hydrogen ion is short-lived and combines with an H2O
molecule to form a hydronium ion (H3O+).

The equilibrium constant of a chemical reaction is given by the ratio
of products to reactants at equilibrium. For the general chemical equation
X + Y ---> A + B, we can write the equilibrium
constant as

For the dissociation of water we get

The equilibrium constant for the dissociation of water at 25°
C has been measured as Keq=1.8x10-16. This number
is small because only a small fraction of water molecules dissociate. The
concentration of water can be determined from the fact that 1 mole of water
weighs 18g and 1 liter of water weighs 1000g. Hence, the concentration
of pure water [H2O] is 1000g/L ¸
18 g/mol = 55.5 mol/L. By substituting these into the above equation, we
find that

[H+][OH-]=1x10-14

In pure water, the concentrations of hydrogen and hydroxide ions are
about the same. Hence by taking the square root of 1x10-14 we
find that [H+] and [OH-] are each about 10-7
M. This means that 1 liter of pure water contains about one ten-millionth
of a mole of hydrogen or hydroxide ions.

Other molecules, however, have the ability to donate or accept hydrogen
ions. Consequently, when other substances are dissolved in water, the concentrations
of H+ and OH- can change. As the concentration of
hydrogen ions increases, the concentration of free hydroxide ions decreases
in order to maintain an equilibrium.

A convenient way to characterize aqueous solutions is to look at the
hydrogen ion concentration. The pH scale allows biologists to define chemical
solutions more conveniently:

pH = -log[H+]

This method is convenient because it eliminates the need for exponential
notation.

We can see how pH changes with hydrogen ion concentration by plotting
the equation for pH as a logarithmic function of [H+].

We can more clearly see how [H+] affects pH by plotting this
graph on a semi-log scale. This will make it easier for us to see values
of pH at very low values of [H+].

In the simplest terms, the value of pH simply gives us the absolute
value of the exponent of the hydrogen ion concentration.

On the pH scale, a 7 is considered to be neutral. Substances that can
donate hydrogen ions, thus increasing [H+], are acids. Strong
acids have pH much lower than 7. Molecules that accept hydrogen ions, thus
decreasing [H+], are bases and have pH higher than 7. Some examples
are given in the graph.

Buffers

Introduction: Cells must constantly maintain their pH in order
to function properly. In animals, for example, the maintainence of blood
pH is crucial for life. A slightly acidic pH (6.95) would result in coma
and death. A slightly more basic pH (7.7) would result in convulsions and
muscle spasms. As another example, the pH of cellular organelles such as
lysosomes (around 5) is lower than the pH of the cytoplasm (around 7.2).
Lysosomes contain enzymes that function optimally in an acidic environment.
Such an acidic environment, however, would be detrimental to biological
processes in the cytoplasm. Each must maintain the appropriate pH.

Methods: Cells can maintain pH chemically by using buffers. Buffers
are molecules that easily interconvert between acidic and basic forms,
donating or accepting protons as conditions change. The dissociation of
a simple acid HA can be described by the following chemical reaction:

HA --->
H+ + A-

We can interpret this as a weak acid (HA) dissociating to form a hydrogen
ion (H+) and a conjugate base (A-). Notice the reverse
happens as well. Buffer solutions are typically mixtures of a weak acid
and its conjugate base. Suppose we were to add a strong base, NaOH, to
the buffer solution. NaOH would raply dissociate into Na+ and
OH- ions. The hydroxide ions would rapidly accept the H+
ions formed by the buffer. Similarly, if we added a strong acid, the conjugate
base, A-, would take up the additional hydrogen ions. In either case, the
buffer (HA) would then continue to dissociate in order to maintain its
original equilibrium.

Buffering ability depends on the ratio of conjugate base concentration
to weak acid concentration. Additionally, the degree of dissociation depends
on the pH of the solution. We can understand this better by deriving the
Henderson-Hasselbalch equation.

The equilibrium constant for the dissociation of a weak acid is given
by

The Henderson-Hasselbalch equation is derived from this by taking the
logarithm of both sides and rearranging to get

We can rewrite -log[H+] as pH and -logKa as pKa
to get the following equation:

We can think of the pKa as the pH at which the number of
molecules of conjugate base [A-] and weak acid [HA] are equal. Thus we
get log[1] = 0 and pKa = pH. We can interpret the above equation
in the following way: pH is a function depending on the constant, pKa,
as well as the ratio of conjugate base to weak acid, [A-]/[HA].

By rearranging the Henderson-Hasselbalch equation slightly, we can calculate
the degree of dissociation of an acid (d) if both the pH of the solution
and the pKa of the acid are known:

where d = [HA] / ([A-]+[HA]). In other words, d is the fraction
of weak acid-conjugate base mixture that is undissociated weak acid. We
will plot pH as a function of d for a pKa = 7.2.

Interpretation: Suppose we have a solution of acid or base at
its pKa value. This means the concentrations of weak acid and
conjugate base are equal, or d = 0.5. Notice the curve around this value
is relatively flat. If we add additional acid or base, the fraction of
undissociated buffer would change in order to maintain an equillibrium.
However, because the curve is relatively flat, the pH of the solution would
increase or decrease only slightly. This ability of an acid or base to
prevent the pH of a solution from changing drastically is called buffering.

We can see from the graph that the buffering ability of a weak acid
or base depends on the fraction dissociated. The buffering ability is highest
when the conjugate base [A-] and weak acid [HA] are present in equal concentrations
(d = 0.5). If d is much higher or lower than 0.5, then additional acid
or base will result in a more dramatic change in pH.

For example, phosphoric acid is physiologically important in cells.
Part of the dissociation or phosphoric acid can be described by the following
equation:

H2PO4- --->
HPO42- + H+

This dissociation has a pKa of 7.2. In an acidic solution,
a high fraction of this acid would be undissociated (low concentration
of conjugate base). We can see from the above graph, that if d = 0.9, the
addition of acid or base would lead to a dramatic change in pH. In cells,
however, phosphate ions are present in considerable quantities. Additionally,
the pH of cellular cytoplasm is approximately 7.2. At this pH, H2PO4-
has a very high buffering capacity. In fact, phosphate ions play an important
role in maintaining, through their buffering ability, the pH of the cytoplasm.

Conclusions: Because water is the universal solvent for all life,
it is important to know how its chemical properties can affect cells. One
of the most important characterizations of a biological fluid is its pH.
The concentration of hydrogen and hydroxide ions in an aqueous solution
can greatly affect both the structure and chemical reactivity of cellular
molecules. Cells are cell organelles must maintain an appropriate pH in
order to function optimally. Additionally, dramatic shifts in pH can play
a role in controlling cellular activities such as egg division after fertilization.
Consequently, cells must work constantly to maintain an acid-base balance.
At the appropriate pH and concentration, buffers can be highly important
in maintaining pH by preventing drastic changes.

Additional Questions:

1. The pH of cellular cytoplasm is normally about 7.2. Cell organelles,
such as lysosomes, have a much lower pH of around 5. What is the hydrogen
ion concentration for each of these? How many times higher is the [H+]
of lysosomes than of cytoplasm?

2. Use rules of logarithms to derive the Henderson-Hasselbalch equation.